Discussion of Homotopy Type Theory and Univalent Foundations
 help / color / mirror / Atom feed
* [HoTT] Dependent path composition in ordinary higher category theory
@ 2020-02-28 18:33 Noah Snyder
  2020-02-28 18:44 ` [HoTT] " Noah Snyder
  0 siblings, 1 reply; 3+ messages in thread
From: Noah Snyder @ 2020-02-28 18:33 UTC (permalink / raw)
  To: Homotopy Type Theory

[-- Attachment #1: Type: text/plain, Size: 1698 bytes --]

Section 2.3 of the book introduces "dependent paths" (which are paths in a
fibration "lying over" a path in the base) and "dependent path composition"
which composes such dependent paths when that makes sense.  I'm working on
a paper that's not about HoTT but where "dependent path composition" plays
an important role.  The problem I'm running into is that I don't know what
dependent path composition is called in "standard" mathematics.  Does
anyone know if this has another name in higher category theory?
 (Naturally, we'll include a remark mentioning the HoTT way of thinking
about this (since it's how I think about it!), but I think that won't be
illuminating to most of our target audience.)

The simplest example of what I have in mind here is if C is a category and
F is an endofunctor and c is an F-algebra (i.e. we have endowed c with a
chosen map f: F(c) --> c) then c is also an F^n-algebra by taking the "nth
power of f" which actually means f \circ F(f) \circ F^2(f) \circ ... \circ
F^{n-1}(f).  In particular, I think this example illustrates that you can
talk about "dependent k-morphisms" and their compositions without requiring
anything in sight to be a (higher) groupoid.

My best guess is that the right setting might be "indexed (higher)
categories"?

Best,

Noah

-- 
You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAO0tDg7uSiQrU8%2B0tnwJQHB_AWvRKAxmAePF88GOvd_ra%3DrpwA%40mail.gmail.com.

[-- Attachment #2: Type: text/html, Size: 2226 bytes --]

^ permalink raw reply	[flat|nested] 3+ messages in thread

end of thread, other threads:[~2020-03-02  7:03 UTC | newest]

Thread overview: 3+ messages (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2020-02-28 18:33 [HoTT] Dependent path composition in ordinary higher category theory Noah Snyder
2020-02-28 18:44 ` [HoTT] " Noah Snyder
2020-03-02  7:03   ` Michael Shulman

This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).